Question

Спростіть вираз:2c/(c+3)-(c-3)/(2c+6)×36/(c^2-3c)

Answer 1

$\displaystyle\frac{2c}{c+3} -\frac{c-3}{2c+6} *\frac{36}{c^2-3c} =\frac{2c}{c+3} -\frac{c-3}{2(c+3)} *\frac{36}{c(c-3)} =\frac{2c}{c+3} -\frac{1}{c+3} *\frac{18}{c} =\\\\\\=\frac{2c}{c+3} -\frac{18}{c(c+3)} =\frac{2c^2-18}{c(c+3)} =\frac{2(c^2-9)}{c(c+3)} =\frac{2(c-3)(c+3)}{c(c+3)} =\frac{2(c-3)}{c} =\\\\\\=\frac{2c-6}{c}=\frac{2(c-3)}{c}$